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Arithmetic Teaching Apparatus

Tests

Throughout most of the nineteenth century, teachers tested the progress of students with oral examinations, often held at the blackboard. By the end of the century, more formal written examinations were used in some states to test graduates of academies in high schools and to accredit teachers. A few universities began to offer advanced degrees in education, and faculty there reflected on the history of mathematics education in this country.

At the same time, as the number of students attending school expanded, as high schools began to offer vocational training, and as manufacturing became more efficient, several authors worried about maximizing the efficiency of schools. A variety of standardized examinations were introduced to predict the performance of students, to point up areas where they needed work, and to evaluate school systems.

The Regents of the University of the State of New York began planning examinations to test the accomplishments of students leaving high schools and academies in the 1860s, and continue to give such examinations today. These examples of the Regents Examinations date from between 1907 and 1919. They were collected by Brooklyn high school mathematics teacher L. Leland Locke.

The tests are:

1. Arithmetic, June 18, 1907 (sheet)

2. Advanced Arithmetic, June 18, 1907 (sheet)

3. Elementary Algebra, June 17, 1907 (sheet)

4. Intermediate Algebra, June 17, 1907 (sheet)

5. Advanced Algebra, June 17, 1907 (sheet)

6. Plane Geometry, June 18, 1907 (sheet)

7. Solid Geometry, June 17, 1907 (sheet)

8. Trigonometry, June 18, 1907 (sheet)

9. Elementary Algebra, January 18, 1915 (sheet)

10. Plane Geometry, June 15, 1915 (sheet)

11. Elementary Algebra, January 23, 1917 (sheet)

12. Plane Geometry, January 24, 1918 (sheet)

13. Elementary Algebra, January 22, 1918 (sheet)

14. Plane Geometry, January 23, 1919 (sheet)

Also included under the number (subindex number .15) is a sheet with handwritten equations.

Reference:

Nancy Beadie, “From Student Markets to Credential Markets: The Creation of the Regents Examination System in New York State, 1864–1890,” History of Education Quarterly, 39, no. 1 (Spring, 1999), pp. 1–30.

In 1843, the New York State Legislature authorized the state superintendent of schools to set examinations and issue certificates to teachers that were valid statewide. New York was the first state to do this. The law was modified several times over the next few years. By 1909, the Education Department of the State of New York had a complex system of certificates, with separate licenses for college graduates, for graduates of state teacher training schools, and for experienced teachers who did not have these academic qualifications.

Brooklyn mathematics teacher L. Leland Locke collected Training School Certificate examinations given between 1911 and 1928. Until 1914, these tests were given by the Education Department of the State of New York. From 1914 onward they are listed as given by the State University of New York. Included in this collection are some 32 tests and groups of tests, namely:

1. Geography / Physiology and Hygiene, January 19, 1911(sheet)

2. Drawing, June 1911 (sheet)

3. American History with Civics / Reading, Writing and Spelling, January 15,1912 (sheet)

4. Arithmetic, January 16,1912 (sheet)

5. Drawing, January 19, 1912 (sheet)

6. History of Education, January 19, 1912 (sheet)

7. Language, Composition and Grammar, January 16, 1912 (sheet)

8. School Management, January 17, 1912 (sheet)

9. American History with Civics / Reading, Writing, and Spelling, June 16, 1913 (sheet)

This paperbound monograph describes the history of arithmetic teaching in the United States to its time of issue, with particular emphasis on the work and influence of William Colburn. The author, Walter Scott Monroe (1882–1961), was professor of school administration at the Kansas State Normal School. He went on to take an active interest in the development of educational tests (see MA*316371.045) .

The monograph was issued by the Bureau of Education of the United States Department of the Interior. This copy was the property of L. Leland Locke, a Brooklyn mathematics teacher and an historian of mathematics.

This collection of tests for students in grades six, seven and eight is an early example of a paper and pencil standardized examination for school children. Included (printed to be read going one direction) are seven tests collectively designed to measure general intelligence. They include multiple choice tests of analogies, arithmetic word problems, vocabulary, matching symbols to numerals (called substitution), verbal ingenuity, arithmetical ingenuity, and synonyms and antonyms. A test of silent reading ability and seven tests of operations of arithmetic are printed to be read going in the other direction.

These tests were developed at the Bureau of Educational Research at the University of Illinois by Walter S. Monroe and B. R. Buckingham. They were published by The Public School Publishing Company of Bloomington, Illinois, and also are known as the Illinois Examination. This version is copyrighted 1920.

This example of the test is from the collection of clinical psychologist David Shakow.

This paper and pencil arithmetic examination was part of the first (1922) edition of a set of tests developed at Stanford University by professor of psychology Lewis M. Terman, statistician and assistant professor of education Truman L. Kelley, and doctoral student Giles M. Ruch (Stanford PhD., 1922). World Book Company published the tests. Scores on the arithmetic examination are divided into two parts: computation of numerical examples, and word problems.

The Stanford Achievement Tests were designed to test the accomplishments of school children in grades two through eight. Editions of the examinations are still in print.

This example of the test is from the collection of clinical psychologist David Shakow.

Reference:

Stanford University, Annual Report of the President of Stanford University, Stanford University: By the University, 1922, pp. 186, 281.

Just before World War I, Stuart A. Courtis, a teacher at a private school for girls in Detroit, Michigan, developed the first widely available standardized tests of arithmetic. His goal was to measure the efficiency of entire schools, not the intellectual ability of a few students.

Courtis went on to become supervisor of educational research in the Detroit public schools. There he developed a set of lesson cards in arithmetic for students in the third through eighth grades. The tests were originally published under his name by World Book Company.

This is a teacher’s manual for a later edition of the drill cards. Courtis’s name does not appear. Courtis withdrew his arithmetic tests from the market in 1938 because he had come to doubt their validity.

The manual was the property of Brooklyn school teacher L. Leland Locke.

Guy T. Buswell and Lenore John published this chart in about 1925 through the Public School Publishing Company of Bloomington, Illinois. The entire package included directions, a pupil's work sheet, a teacher's diagnostic chart, and a pupil's work sheet diagnostic chart. This is the pupil's work sheet. It lists problems in addition, subtraction, multiplication and division.

At the time of the publication, Buswell was in the Department of Education at the University of Chicago and John was at the University of Chicago Laboratory Schools. Buswell and John hoped that their chart would be used to determine the areas of arithmetic in which a student required further work. It served as a “diagnosis” of problems rather than a “prognosis” of future achievement. In later years, Buswell and John collaborated on a series of arithmetic textbooks.

This example of the test is from the personal collection of U. S. government psychologist and university teacher in education Samuel Kavruck.

For a related object , the teacher's diagnostic chart, see 1990.0034.162

Guy T. Buswell and Lenore John published this chart in about 1925 through the Public School Publishing Company of Bloomington, Illinois. The entire package included directions, a pupil's work sheet, a teacher's diagnostic chart, and a pupil's work sheet diagnostic chart. This is the teacher’s diagnostic chart. It includes not only arithmetic problems, but space for observation notes on the pupil’s work. There also is a list of possible erroneous habits for each operation of arithmetic, with a space for checking off habits observed.

At the time of the publication, Buswell was in the Department of Education at the University of Chicago and John was at the University of Chicago Laboratory Schools. Buswell and John hoped that their chart would be used to determine the areas of arithmetic in which a student required further work. It was a “diagnosis” of problems rather than a “prognosis” of future achievement. In later years, Buswell and John collaborated on a series of arithmetic textbooks.

This example of the test is from the personal collection of U. S. government psychologist and university teacher in education Samuel Kavruck.

By the 1920s, mathematics educators increasingly turned to standardized tests as a way to measure what students knew, to predict what they could learn, and to determine where they had difficulties. This test had sections on addition, subtraction, multiplication, and division. The final two sections were on fractions, decimals, and percentages; and on a combination of problems. The authors were Raleigh Schorling (1887–1950), John R. Clark (1887–1986), and Mary A. Potter (1889–1993?). World Book Company published the four page leaflet in 1928. Versions of the test would be published for decades.

By 1926, when the test was first published, Schorling and Clark had obtained their PhDs from Teacher’s College of Columbia University. After earning his doctorate, Clark headed the mathematics department of the Chicago State Teacher’s College, and then in 1920 returned to teach in the Department of Mathematics Education at Teacher’s College. He remained there until his retirement in 1952.

Schorling taught at the Lincoln School of Teacher’s College. He left in 1923 to become the first principal of the University High School at the University of Michigan, and completed his Teacher’s College doctorate in 1924. He remained at Ann Arbor for the rest of his career, serving as well as a professor of education at the university. Mary Potter obtained her undergraduate degree from Lawrence College in Appleton, Wisconsin, in 1913. She taught in several Wisconsin school districts, settling in Racine by 1920 and living there the rest of her working life.

At the Lincoln School, Schorling and Clark worked to reform arithmetic education by emphasizing the affairs of daily life. Their efforts led them to author new textbooks as well as new tests. Schorling, Clark, and Potter were all active in the establishment of the National Council of Teachers of Mathematics in 1920.

Bruce V. Moore (1891—1977), an industrial psychologist at Pennsylvania State College (later Pennsylvania State University) published this test leaflet in 1941. It consists of twenty word problems involving use of arithmetic, with spaces for writing the answer.

This is one of a series of psychological tests given to the Smtihsonian by Cincinnati Boss Company.

Reference:

For Moore’s autobiography, see the website of the Society for Industrial and Organizational Psychology at: http://www.siop.org/presidents/Moore.aspx.